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When evaluating the base cost of a card, you might be tempted to say that most of the cost lives in the base attributes; so how would you evaluate that statement for truthiness?

Looking at a linear regression fit from all Minions with an expressed cost >0:

Linear regression model of all Minion cards with mana cost > 0

First, just look at the quantization in the residuals-vs-fitted. Pretty, isn't it? That suggests that the mechanics associated with these cards have clear, distinguishable values; this is Blizzard's own statisticians at work.

Next is the fit to a normal distribution; not bad, and as you'd expect, the outliers are the ones whose mechanics strongly influence mana cost (in either direction).

So a basic LM fit is surprisingly expressive - moreso by far than I was expecting, and it matches Trump's views on base cost of card being a very important factor. In fact, even without filtering out all of the cards that represent more unusual cases, it covers more than 76% of the variance in the dataset.

We can do better, though - if we're looking to fit a model for base cost, let's restrict the model to those mechanics that don't actually express any other mechanics.

In other words, let's go build a linear model that fits only the relationship between Mana, Attack, and Health for minions with no other mechanics.

Linear regression model of all Minion cards with mana cost > 0 and no other mechanics.

The resulting fit is better, too - We're at 93% of the variance of the data covered by the model.